登录
TensorFlow 1 version
|
View source on GitHub
|
Computes the approximate AUC (Area under the curve) via a Riemann sum.
Inherits From: Metric, Layer, Module
tf.keras.metrics.AUC(
num_thresholds=200, curve='ROC',
summation_method='interpolation', name=None, dtype=None,
thresholds=None, multi_label=False, label_weights=None
)
Used in the notebooks
| Used in the tutorials |
|---|
This metric creates four local variables, true_positives, true_negatives,
false_positives and false_negatives that are used to compute the AUC.
To discretize the AUC curve, a linearly spaced set of thresholds is used to
compute pairs of recall and precision values. The area under the ROC-curve is
therefore computed using the height of the recall values by the false positive
rate, while the area under the PR-curve is the computed using the height of
the precision values by the recall.
This value is ultimately returned as auc, an idempotent operation that
computes the area under a discretized curve of precision versus recall values
(computed using the aforementioned variables). The num_thresholds variable
controls the degree of discretization with larger numbers of thresholds more
closely approximating the true AUC. The quality of the approximation may vary
dramatically depending on num_thresholds. The thresholds parameter can be
used to manually specify thresholds which split the predictions more evenly.
For best results, predictions should be distributed approximately uniformly
in the range [0, 1] and not peaked around 0 or 1. The quality of the AUC
approximation may be poor if this is not the case. Setting summation_method
to 'minoring' or 'majoring' can help quantify the error in the approximation
by providing lower or upper bound estimate of the AUC.
If sample_weight is None, weights default to 1.
Use sample_weight of 0 to mask values.
Args | |
|---|---|
num_thresholds
|
(Optional) Defaults to 200. The number of thresholds to use when discretizing the roc curve. Values must be > 1. |
curve
|
(Optional) Specifies the name of the curve to be computed, 'ROC' [default] or 'PR' for the Precision-Recall-curve. |
summation_method
|
(Optional) Specifies the Riemann summation method used.
'interpolation' (default) applies mid-point summation scheme for ROC.
For PR-AUC, interpolates (true/false) positives but not the ratio that
is precision (see Davis & Goadrich 2006 for details);
'minoring' applies left summation
for increasing intervals and right summation for decreasing intervals;
'majoring' does the opposite.
|
name
|
(Optional) string name of the metric instance. |
dtype
|
(Optional) data type of the metric result. |
thresholds
|
(Optional) A list of floating point values to use as the
thresholds for discretizing the curve. If set, the num_thresholds
parameter is ignored. Values should be in [0, 1]. Endpoint thresholds
equal to {-epsilon, 1+epsilon} for a small positive epsilon value will
be automatically included with these to correctly handle predictions
equal to exactly 0 or 1.
|
multi_label
|
boolean indicating whether multilabel data should be treated as such, wherein AUC is computed separately for each label and then averaged across labels, or (when False) if the data should be flattened into a single label before AUC computation. In the latter case, when multilabel data is passed to AUC, each label-prediction pair is treated as an individual data point. Should be set to False for multi-class data. |
label_weights
|
(optional) list, array, or tensor of non-negative weights
used to compute AUCs for multilabel data. When multi_label is True,
the weights are applied to the individual label AUCs when they are
averaged to produce the multi-label AUC. When it's False, they are used
to weight the individual label predictions in computing the confusion
matrix on the flattened data. Note that this is unlike class_weights in
that class_weights weights the example depending on the value of its
label, whereas label_weights depends only on the index of that label
before flattening; therefore label_weights should not be used for
multi-class data.
|
Standalone usage:
m = tf.keras.metrics.AUC(num_thresholds=3)m.update_state([0, 0, 1, 1], [0, 0.5, 0.3, 0.9])# threshold values are [0 - 1e-7, 0.5, 1 + 1e-7]# tp = [2, 1, 0], fp = [2, 0, 0], fn = [0, 1, 2], tn = [0, 2, 2]# recall = [1, 0.5, 0], fp_rate = [1, 0, 0]# auc = ((((1+0.5)/2)*(1-0))+ (((0.5+0)/2)*(0-0))) = 0.75m.result().numpy()0.75
m.reset_states()m.update_state([0, 0, 1, 1], [0, 0.5, 0.3, 0.9],sample_weight=[1, 0, 0, 1])m.result().numpy()1.0
Usage with compile() API:
model.compile(optimizer='sgd', loss='mse', metrics=[tf.keras.metrics.AUC()])
Attributes | |
|---|---|
thresholds
|
The thresholds used for evaluating AUC. |
Methods
interpolate_pr_auc
interpolate_pr_auc()
Interpolation formula inspired by section 4 of Davis & Goadrich 2006.
https://www.biostat.wisc.edu/~page/rocpr.pdf
Note here we derive & use a closed formula not present in the paper as follows:
Precision = TP / (TP + FP) = TP / P
Modeling all of TP (true positive), FP (false positive) and their sum P = TP + FP (predicted positive) as varying linearly within each interval [A, B] between successive thresholds, we get
Precision slope = dTP / dP = (TP_B - TP_A) / (P_B - P_A) = (TP - TP_A) / (P - P_A) Precision = (TP_A + slope * (P - P_A)) / P
The area within the interval is (slope / total_pos_weight) times
int_A^B{Precision.dP} = int_A^B{(TP_A + slope * (P - P_A)) * dP / P} int_A^B{Precision.dP} = int_A^B{slope * dP + intercept * dP / P}
where intercept = TP_A - slope * P_A = TP_B - slope * P_B, resulting in
int_A^B{Precision.dP} = TP_B - TP_A + intercept * log(P_B / P_A)
Bringing back the factor (slope / total_pos_weight) we'd put aside, we get
slope * [dTP + intercept * log(P_B / P_A)] / total_pos_weight
where dTP == TP_B - TP_A.
Note that when P_A == 0 the above calculation simplifies into
int_A^B{Precision.dTP} = int_A^B{slope * dTP} = slope * (TP_B - TP_A)
which is really equivalent to imputing constant precision throughout the first bucket having >0 true positives.
| Returns | |
|---|---|
pr_auc
|
an approximation of the area under the P-R curve. |
reset_states
reset_states()
Resets all of the metric state variables.
This function is called between epochs/steps, when a metric is evaluated during training.
result
result()
Computes and returns the metric value tensor.
Result computation is an idempotent operation that simply calculates the metric value using the state variables.
update_state
update_state(
y_true, y_pred, sample_weight=None
)
Accumulates confusion matrix statistics.
| Args | |
|---|---|
y_true
|
The ground truth values. |
y_pred
|
The predicted values. |
sample_weight
|
Optional weighting of each example. Defaults to 1. Can be a
Tensor whose rank is either 0, or the same rank as y_true, and must
be broadcastable to y_true.
|
| Returns | |
|---|---|
| Update op. |